Classical and Quantum Algorithms for Exponential Congruences -- Quantum Algorithms for Evaluating Min-Max Trees -- Irreversibility of Entanglement Loss -- Quadratic Form Expansions for Unitaries -- Improved Constructions of Quantum Automata -- An Application of the Deutsch-Jozsa Algorithm to Formal Languages and the Word Problem in Groups -- An Elementary Optical Gate for Expanding Symmetrically Shared Entanglement -- Security Bounds for Quantum Cryptography with Finite Resources -- On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography -- Architecture of a Quantum Multicomputer Implementing Shor’s Algorithm.

This book constitutes the thoroughly refereed post-workshop proceedings of the Third Workshop on Theory of Quantum Computation, Communication, and Cryptography, TQC 2008, held in Tokyo, Japan, in January/February 2008. The 10 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers present current original research and focus on theoretical aspects of quantum computation, quantum communication, and quantum cryptography, which are part of a larger interdisciplinary field that casts information science in a quantum mechanical framework.